If a patient requires 500 mg of acetaminophen, how many ml of a 160 mg/5 ml solution does the patient need?

To determine how many milliliters of a 160 mg/5 ml solution are needed to provide a dose of 500 mg of acetaminophen, you can set up a ratio based on the concentration provided.

The solution concentration is 160 mg in 5 ml, which can be translated into a simple unit conversion to see how many milligrams are present in each milliliter. From the concentration, you can calculate the amount of acetaminophen per ml:

[

\frac{160 \text{ mg}}{5 \text{ ml}} = 32 \text{ mg/ml}

]

Next, to find out how many milliliters are required to deliver a dose of 500 mg, you can use the following calculation:

[

\text{Volume required (ml)} = \frac{\text{Desired dose (mg)}}{\text{Concentration (mg/ml)}}

]

Plugging in the numbers:

[

\text{Volume required (ml)} = \frac{500 \text{ mg}}{32 \text{ mg/ml}} = 15.625 \text{ ml}

]

Since 15.625 ml rounds to 16 ml, this is the correct amount of solution needed